Question: The sum of two numbers is $108$, and their difference is $76$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 108}$ ${x-y = 76}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 184 $ $ x = \dfrac{184}{2} $ ${x = 92}$ Now that you know ${x = 92}$ , plug it back into $ {x+y = 108}$ to find $y$ ${(92)}{ + y = 108}$ ${y = 16}$ You can also plug ${x = 92}$ into $ {x-y = 76}$ and get the same answer for $y$ ${(92)}{ - y = 76}$ ${y = 16}$ Therefore, the larger number is $92$, and the smaller number is $16$.